Skip to main content
Log in

On a class of new KKM theorem with applications

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper, a class of new KKM theorem is obtained which unifies and improves the corresponding results in [2], [3], [6], [7], [11]. As applications, we utilize our result to obtain some matching theorem, coincidence theorem, fixed point theorem, minimax inequality theorem and section theorem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C., Bardaro and R., Ceppitelli, Some further generalization of Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities, J. Math. Anal. Appl., 132 (1988), 484–490.

    Google Scholar 

  2. Chang, Shihsen and Zhang, Ying, Generalized KKM theorem and variational inequalities. J. Math. Anal. Appl., 159 (1991), 208–223.

    Google Scholar 

  3. Chang, Shihsen and Ma, Yihai, Generalized KKM theorem on H-space with applications, J. Math. Anal. Appl., 163 (1992), 406–421.

    Google Scholar 

  4. Chang, Shihsen, Variational Inequality and Complementarity Problem Theory with Applications, Shanghai Sci. and Tech. Literature Publishing House, Shanghai (1991). (in Chinese)

    Google Scholar 

  5. Ky, Fan, Some properties of convex sets related to fixed point theorems, Math. Ann., 266 (1984), 519–537.

    Google Scholar 

  6. Ky, Fan, A generalization of Tychonoff's fixed point theorems, Math. Ann., 42 (1961), 303–310.

    Google Scholar 

  7. C. Horvath, Some results on multi-valued mappings and inequalities without convexity, in “Nonlinear and Convex Analysis”, Lecture Notes in Pure and Appl. Math. Ser. V. 107 Springer Verlag, (1987).

  8. W. K., Kim, Some applications of the Kakutani fixed point theorem, J. Math. Anal. Appl., 121 (1987). 119–122.

    Google Scholar 

  9. B., Knaster, B., Kuratowski and S., Mazurkiewicz, Ein beweis des fixpunktsatzas fur n-dimensionale simplexe, Fund. Math., 14 (1929), 132–137.

    Google Scholar 

  10. M., Lassonde, On the use of KKM multifunctions in fixed point theory and related topic. J. Math. Anal. Appl., 97 (1983), 151–201.

    Google Scholar 

  11. S., Park, Generalizations of Ky Fan's matching theorems and their applications, J. Math. Anal. Appl., 141 (1989), 164–176.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Project supported by the National Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shisheng, Z., Xian, Z. On a class of new KKM theorem with applications. Appl Math Mech 17, 819–826 (1996). https://doi.org/10.1007/BF00127181

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00127181

Key words

Navigation